{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Implementation of Lotka-Volterra using Euler and `run_ode_solver`\n",
    "\n",
    "Copyright 2018 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Euler with implicit `dt=1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(system, update_func):\n",
    "    \"\"\"Runs a simulation of the system.\n",
    "        \n",
    "    system: System object\n",
    "    update_func: function that updates state\n",
    "    \n",
    "    returns: TimeFrame\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    \n",
    "    frame = TimeFrame(columns=init.index)\n",
    "    frame.row[t0] = init\n",
    "    \n",
    "    for t in linrange(t0, t_end):\n",
    "        frame.row[t+1] = update_func(frame.row[t], t, system)\n",
    "    \n",
    "    return frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_func(state, t, system):\n",
    "    \"\"\"Update the Lotka-Volterra model.\n",
    "    \n",
    "    state: State(x, y)\n",
    "    t: time\n",
    "    system: System object\n",
    "    \n",
    "    returns: State(x, y)\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    x, y = state\n",
    "\n",
    "    dxdt = alpha * x - beta * x * y\n",
    "    dydt = delta * x * y - gamma * y\n",
    "    \n",
    "    x += dxdt\n",
    "    y += dydt\n",
    "    \n",
    "    return State(x=x, y=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "x    1\n",
       "y    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "init = State(x=1, y=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>0.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>beta</th>\n",
       "      <td>0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma</th>\n",
       "      <td>0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>delta</th>\n",
       "      <td>0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t0</th>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>200.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "alpha      0.05\n",
       "beta       0.10\n",
       "gamma      0.10\n",
       "delta      0.10\n",
       "t0         0.00\n",
       "t_end    200.00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = System(alpha=0.05,\n",
    "                beta=0.1,\n",
    "                gamma=0.1,\n",
    "                delta=0.1,\n",
    "                t0=0,\n",
    "                t_end=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>0.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "x    0.95\n",
       "y    1.00\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "update_func(init, 0, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.95</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.9025</td>\n",
       "      <td>0.995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.857826</td>\n",
       "      <td>0.985299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.816196</td>\n",
       "      <td>0.97129</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            x         y\n",
       "0.0         1         1\n",
       "1.0      0.95         1\n",
       "2.0    0.9025     0.995\n",
       "3.0  0.857826  0.985299\n",
       "4.0  0.816196   0.97129"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = run_simulation(system, update_func)\n",
    "results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa73f3c7c88>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using the ODE solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"Compute slopes for the Lotka-Volterra model.\n",
    "    \n",
    "    state: State(x, y)\n",
    "    t: time\n",
    "    system: System object\n",
    "    \n",
    "    returns: pair of derivatives\n",
    "    \"\"\"\n",
    "    unpack(system)\n",
    "    x, y = state\n",
    "\n",
    "    dxdt = alpha * x - beta * x * y\n",
    "    dydt = delta * x * y - gamma * y\n",
    "    \n",
    "    return dxdt, dydt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "system.set(init=init, t_end=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sol</th>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_events</th>\n",
       "      <td>[]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nfev</th>\n",
       "      <td>134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>njev</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nlu</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>status</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>The solver successfully reached the end of the...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sol                                                      None\n",
       "t_events                                                   []\n",
       "nfev                                                      134\n",
       "njev                                                        0\n",
       "nlu                                                         0\n",
       "status                                                      0\n",
       "message     The solver successfully reached the end of the...\n",
       "success                                                  True\n",
       "dtype: object"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results, details = run_ode_solver(system, slope_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa72c15b9b0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sol</th>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_events</th>\n",
       "      <td>[]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nfev</th>\n",
       "      <td>608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>njev</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nlu</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>status</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>The solver successfully reached the end of the...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sol                                                      None\n",
       "t_events                                                   []\n",
       "nfev                                                      608\n",
       "njev                                                        0\n",
       "nlu                                                         0\n",
       "status                                                      0\n",
       "message     The solver successfully reached the end of the...\n",
       "success                                                  True\n",
       "dtype: object"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.set(init=init, t_end=200)\n",
    "results, details = run_ode_solver(system, slope_func, max_step=2)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa72c06cf60>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Euler, running for a longer duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>0.95</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0</th>\n",
       "      <td>0.9025</td>\n",
       "      <td>0.995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.0</th>\n",
       "      <td>0.857826</td>\n",
       "      <td>0.985299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.0</th>\n",
       "      <td>0.816196</td>\n",
       "      <td>0.97129</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            x         y\n",
       "0.0         1         1\n",
       "1.0      0.95         1\n",
       "2.0    0.9025     0.995\n",
       "3.0  0.857826  0.985299\n",
       "4.0  0.816196   0.97129"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.set(t_end=2000)\n",
    "results = run_simulation(system, update_func)\n",
    "results.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa72c052240>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Running the ODE solver for a longer duration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>sol</th>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_events</th>\n",
       "      <td>[]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nfev</th>\n",
       "      <td>1172</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>njev</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nlu</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>status</th>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>The solver successfully reached the end of the...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "sol                                                      None\n",
       "t_events                                                   []\n",
       "nfev                                                     1172\n",
       "njev                                                        0\n",
       "nlu                                                         0\n",
       "status                                                      0\n",
       "message     The solver successfully reached the end of the...\n",
       "success                                                  True\n",
       "dtype: object"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results, details = run_ode_solver(system, slope_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fa72bfd2630>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
